求解双曲型守恒律的半离散三阶中心迎风格式  

Third-order semi-discrete central-upwind scheme for hyperbolic conservation laws

作　　者：陈建忠[1] 史忠科[1] 

机构地区：[1]西北工业大学自动化学院,西安710072

出　　处：《计算力学学报》2006年第2期157-162,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金重点基金(60134010)资助项目

摘　　要：给出了求解一维双曲型守恒律的一种半离散三阶中心迎风格式,并利用逐维进行计算的方法将格式推广到二维守恒律。构造格式时利用了波传播的单侧局部速度,三阶重构方法的引入保证了格式的精度。时间方向的离散采用三阶TVD R unge-K u tta方法。本文格式保持了中心差分格式简单的优点,即不需用R iem ann解算器,避免了进行特征分解过程。用该格式对一维和二维守恒律进行了大量的数值试验,结果表明本文格式是高精度、高分辨率的。A third-order semi-discrete central-upwind scheme for one-dimensional system of conservation laws was presented. The scheme is extended to two-dimensional hyperbolic conservation law by the dimension-by-dimension approach. The presented scheme is based on the one-sided local speed of wave propagation. In order to guarantee the accuracy of spatial discretizaiton, a third-order reconstruction is introduced in this paper. The time integration is implemented by using the third-order TVD Runge- Kutta method. The resulting scheme retains the main advantage of the central-schemes simplicity, namely no Riemann solvers are involved and hence characteristic decompositions can be avoided. A variety of numerical experiments in both one and two dimensions are computed. The results show the high accuracy and high resolution of the scheme.

关 键 词：双曲型守恒律 中心迎风格式 半离散 重构 

分 类 号：O35[理学—流体力学] O241.82[理学—力学]